This "issue" comes up at least twice a day in this forum.
NO, the watch and the iPhone are not the same device. The iPhone, like the iPad, Mac, or whatever devices you have that receive notifications, check for these notifications periodically. I'm sure it's quite frequent for iPad, iPhone and Mac, but the intervals will vary between the three.
e.g. I have an iPhone, iMac, Ipad, Ipod Touch. When I get a text, the beeps/buzzes often come in at four different intervals over the course of about 20 seconds.
The Watch is a bit different, as it depends on the iPhone and mirrors the notifications. And I'll bet it doesn't check quite as often as other devices in order to save battery power. So the likelihood is the Watch will trail the iPhone by several seconds.
If you have gotten notifications that seem simultaneous between the phone and watch, that's just random luck. It won't, and shouldn't, happen every time.